Parabolic problems with nonlinear boundary conditions and critical nonlinearities

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Abstract

We prove existence, uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions. We study these problems with initial data in Lq(Ω), W1, q(Ω), 1

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Arrieta, J. M., Carvalho, A. N., & Rodríguez-Bernal, A. (1999). Parabolic problems with nonlinear boundary conditions and critical nonlinearities. Journal of Differential Equations, 156(2), 376–406. https://doi.org/10.1006/jdeq.1998.3612

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